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3. Determine the transfer function of the following circuits. (a) Voltage Divider Vi R1 100 L=0.1H wwwm R2=400 www - Vo C=0.02F

3. Determine the transfer function of the following circuits. (a) Voltage Divider Vi R1 100 L=0.1H wwwm R2=400 www - Vo C=0.02F

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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3. Determine the transfer function of the following circuits. (a) Voltage Divider R1 100 L=0.1H vi VW 0.1 F (b) Non-inverting op-amp with voltage divider input 50 Vx R2=400 Vi 100 www x(1) (c) Non-inverting op-amp with voltage divider input milli 20 www 100 Vo = 0.02F m 5002 Vo y(1) The circuit can be regarded as the voltage divider at the input cascaded with the non- inverting amplifier. Vo 4. The input x(t) and the corresponding output y(t) of a linear, time-invariant system are shown as follows: 1.5 Vo Vx H(s)-------------- X ---- Vi Vi (Vo/Vx)-transfer function of the non- inverting amplifier (Vx/Vi)-transfer function of the voltage divider circuit Vx exponential -t,sec. -t,sec. 00.2 Determine the transfer function H(s) and the impulse response h(t) of the system. Note: H(s)=Y(s)/X(s) is a ratio of the output signal Y(s) and its corresponding input signal X(s). Y(s) and X(s) are the Laplace transforms of y(t) and x(t), respectively.
Transcribed Image Text:3. Determine the transfer function of the following circuits. (a) Voltage Divider R1 100 L=0.1H vi VW 0.1 F (b) Non-inverting op-amp with voltage divider input 50 Vx R2=400 Vi 100 www x(1) (c) Non-inverting op-amp with voltage divider input milli 20 www 100 Vo = 0.02F m 5002 Vo y(1) The circuit can be regarded as the voltage divider at the input cascaded with the non- inverting amplifier. Vo 4. The input x(t) and the corresponding output y(t) of a linear, time-invariant system are shown as follows: 1.5 Vo Vx H(s)-------------- X ---- Vi Vi (Vo/Vx)-transfer function of the non- inverting amplifier (Vx/Vi)-transfer function of the voltage divider circuit Vx exponential -t,sec. -t,sec. 00.2 Determine the transfer function H(s) and the impulse response h(t) of the system. Note: H(s)=Y(s)/X(s) is a ratio of the output signal Y(s) and its corresponding input signal X(s). Y(s) and X(s) are the Laplace transforms of y(t) and x(t), respectively.
Problems: 1. A system has a transfer function Vo(s) 50s H(s) = Vi(s) (s+1) (s+10) (a) Determine the steady-state output of the system if the input is vi(t)={5+5sin(t)+5sin(5t)+5sin(10t)+5sin(20t)} u(t) volts. HINT: Determine the steady-state response due to 5u(t), 5sin(t)u(t), 5sin(5t)u(t), and the other input components separately. The resultant output is the sum of the response of the system to each of the input components. Since the required response is steady- state only and the input is expressed in terms of its frequency components, the frequency-response to each component can be determined. (b) What is the type of the frequency response of the system based on the computed steady-state output in (a)? Explain your answer. 2. Given the circuit shown as R1=100 C=0.005F -Ovo R2=900 (a) Determine H(o), H(o), ZH(o). (b) Sketch the magnitude response and phase response of the system. (c) Determine the type of frequency response and the corresponding frequency response specifications. 3. For the following systems, sketch the magnitude response and determine the type of frequency response and the corresponding frequency response specifications. 2(s+500) 2(s+20) (a) H(s) = (b) H(s) = (s+20) (s+500)
Transcribed Image Text:Problems: 1. A system has a transfer function Vo(s) 50s H(s) = Vi(s) (s+1) (s+10) (a) Determine the steady-state output of the system if the input is vi(t)={5+5sin(t)+5sin(5t)+5sin(10t)+5sin(20t)} u(t) volts. HINT: Determine the steady-state response due to 5u(t), 5sin(t)u(t), 5sin(5t)u(t), and the other input components separately. The resultant output is the sum of the response of the system to each of the input components. Since the required response is steady- state only and the input is expressed in terms of its frequency components, the frequency-response to each component can be determined. (b) What is the type of the frequency response of the system based on the computed steady-state output in (a)? Explain your answer. 2. Given the circuit shown as R1=100 C=0.005F -Ovo R2=900 (a) Determine H(o), H(o), ZH(o). (b) Sketch the magnitude response and phase response of the system. (c) Determine the type of frequency response and the corresponding frequency response specifications. 3. For the following systems, sketch the magnitude response and determine the type of frequency response and the corresponding frequency response specifications. 2(s+500) 2(s+20) (a) H(s) = (b) H(s) = (s+20) (s+500)
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